my scientific age

Chapter 70 Peking No. [-] Middle School, Really Poor!
Life in the school tends to be calm. Yu Hua switches back and forth between the roles of a teacher and a student every day, teaching Fang Yu and Zhou Yuan how to draw, tutoring Tan Qing with homework, and reporting to his roommates about portable lighting sources. In this case, the rich Zhou Yuan and Liu Tao may not care about the profits made by the lighting equipment, but not everyone is as unpretentious and rich as the two of them.

Yu Hua and the rest of the roommates are still very concerned about the situation of portable lighting sources. Fortunately, although the heat about the lighting system in the school has dropped slightly, the number of students who come to the second-grade dormitory every night has not decreased. Ordered four light source systems, the unified price is 60 oceans.

Counting Fang Yu's three and Zhang Wen's one, there are eight in total, occupying nearly half of the third-grade dormitory.

this is a good news.

The main supplier Ji Han also received good news. The accessories for the portable lighting source are basically complete and have been placed in a temporarily rented room outside the school. Ji Han's father has arranged for two guards to take care of it.

I have to say, leaning against a big tree is a good way to enjoy the shade.

A few days passed by and disappeared without knowing it. In a blink of an eye, it was the Lantern Festival. The Lantern Festival in 1937 was very dull. There were no activities in the school and nothing was given away.

Well, expecting schools that are so short of funds to be called poor to distribute gifts for the Lantern Festival, it is better to do it yourself.

During the Lantern Festival, everyone specially let go of the busy and tense study rhythm and held a temporary gathering. The powerful sponsors Zhou Yuan and Liu Tao bought exquisite dishes with different characteristics from Dongxing Building and Taifeng Building respectively. A very rare bottle of Lafite red wine, we spent the Lantern Festival together.

The Lafite red wine of this era was still stuck in the mud during the First World War and was at a low point in its historical development. It is far inferior to other famous wineries in Europe, but in China, as long as it is stained with the famous wine of the West, its value will soar. It is a symbol of power and wealth.

However, for Yu Hua, who can't taste wine, any red wine is no good.

After drinking Lafite in 1937, Yu Hua couldn't taste any mysterious taste except for the delicious taste. He could only lament that he had no talent in this area.

People are proficient in everything about eating, drinking, and playing, and they can say three or five articles on a wine.

After the rare Lantern Festival, relax the tense nerves. On the second day, everyone in the second class and second class once again threw themselves into a tense and busy state of study.

Relaxed, it's time to continue learning.

Everyone in the top two dare not forget their responsibilities and obligations as students.

The same is true for Yu Hua, who goes back and forth between the library, the cafeteria and the teaching building every day, living a standard three-point and one-line life, like a greedy and ferocious glutton, constantly absorbing knowledge and improving his scientific research level.

However, people's energy is limited. In the current high school stage, Yu Hua's study route is mainly mathematics, supplemented by chemistry, and the remaining five subjects such as physics and biology are subject to temporarily meeting the independent admissions test of National Tsinghua University.

As time went on, it wasn't long before the second weekend came.

Library, reading room on the second floor, old location.

Yu Hua was sitting on the seat with a straight posture, holding a pen in his right hand, and staring at the real exam paper for the 1936 National Central University Independent Enrollment Examination on the table. This is the real exam paper he just found from Lin Wan next door. Help with two meals.

To this condition, Yu Hua agreed without hesitation. The real exam papers are extremely precious in this era, and there are very few channels to obtain them, let alone the National Central University exam papers.

However, schools are limited by the cost of printing test papers, so they rarely arrange for students to take mock exams. There is no such thing as a small test in three days, a big test in five days, and Saturday and weekend test papers.

Peking No. [-] Middle School is really poor.

But the magic is that the students of Peking No. [-] Middle School are really rich.

On weekdays, Mr. Luo Wenguang, Mr. Ren, would print the test papers at his own expense. As a mathematician, he understands that it is not enough to just look at maths. He must keep doing the questions. However, due to the limited personal ability of Mr., the class is simulated. The number of exams is still few and far between.

In △ABC, if sinB+cosB=√2, what is the maximum value of sin2A/tanB+tanC.

Glancing at the question, the scratch paper was useless, Yu Hua calculated directly in his mind, sketched the graph, and after a second, he wrote the answer without hesitation.

Answer: √2/2-1/2.

Topic passed, next question.

In the plane rectangular coordinate system xOy, A and B are two points on the circle C: (X-1)+y=1, and AB=√2, the coordinates of the point P are (2, 1), then 2|PA→ The value range of -PB→|

[√5-√2, √5+√2]

One second for reviewing questions and two seconds for answering questions. The speed is even more exaggerated than copying homework. The most important thing is that there is no need for scratch paper.

Today's Yu Hua, doing the real test questions has reached the level of saving draft paper, the whole person is calm, and he finishes the questions quickly. .

已知数列{an}满足an+2/an+1=2（n∈N＊），且a1=1/2。

(1) Find the general term formula of the sequence {an},

（1）求数列{an}的前n项和为Sn，求证：当N≥2时，S2n-1-Sn-1＞n-4/5。

This question is interesting.

The difficulty of the question is almost the same as that of the mathematics finale of the later college entrance examination. It seems that the person who asked the question is a master.

Yu Hua looked at the final big question, a smile finally appeared on his expressionless face, carefully reviewed the question, and thought about it, ten seconds later.

因为a1=1/2，且an+1/an+1=2，……

Simply list the proof process, and then use mathematical induction, and soon, the answer will be written.

The general formula for the first sub-question is an=n/n+1.

The second sub-problem is a complex and tedious process of verification. The idea of ​​​​solving the problem is very simple. First prove x∈(0), x>1+lnx, and use the scaling method to prove it. Put it on and you're done.

While thinking and writing, after just a few minutes, the proof process of the last major question and the second sub-question was all written, and the whole real question paper was completed.

"Huh...it should be correct." After finishing the question, Yu Hua took a deep breath, turned to the beginning of the test paper, and re-examined.

Checking the test paper is a matter of attitude, and Yu Hua will not tolerate his own making low-level mistakes, resulting in loss of scores.

After 5 minutes, the entire real test paper was checked, and Yu Hua confirmed that it was correct.

After laying out the test papers, Yu Hua took out the answers to the real test papers from his schoolbag and checked them one by one.

There are a total of five multiple-choice questions, with a total score of [-], all correct.

Fill in the blanks for a total of ten questions, with a total score of [-] points, all correct.

There are seven calculation questions, with a total score of [-], all correct.

In 1936, he scored [-] points in the simulated results of the National Central University's mathematics real exam paper.

Full marks.

(End of this chapter)